I found this titillating equation: $$M = \gamma + \sum_{p} \left[ \ln\! \left( 1 - \frac{1}{p} \right) + \frac{1}{p} \right]$$
where $\displaystyle M=\lim_{n \rightarrow \infty } \left( \sum_{p\,\leq \,n} \frac{1}{p} - \ln(\ln n) \right)$ and $\displaystyle\gamma=\lim_{n \rightarrow \infty } \left( \sum_{k\,=\,1}^n \frac{1}{k} - \ln n \right)$ and $p$ ranges over the prime numbers.
Sadly I am unable to prove it. Can anyone help?